Circular
Acceleration

When an object is in uniform circular motion, there is a
net force and resulting acceleration involved because this is a
non-inertial frame of reference. Textbooks demonstrate that the
acceleration and the resulting net force is directed radially
inward, having a value

ac = v2/R

Any acceleration along the tangent (perpendicular to the
radius) occurs only while speeding up or slowing down. If the
circular motion is uniform, the speed is constant, there is no
tangential acceleration.

OBJECTIVES

Show that the acceleration in constant circular motion is
directed along the radius rather than along the tangent.

Show that centripetal acceleration is directly proportional
to the radius for a rotating platform.

MATERIALS

PRELIMINARY QUESTIONS

If one travels in a circular path at a constant speed,
he/she feels a force. In which direction does this force appear
to be directed? Explain.

If one travels in a circular path at a constant speed, what
is his/her acceleration in their direction of motion? Explain.
What is their direction of motion at any time?

PROCEDURE

Mount the interface and accelerometers as shown in the
diagrams. If possible, mount the outer accelerometer at double
the radius of the inner one. For both accelerometers, the axes
that are aligned with the radius should be pointing the same
direction. Secure the interface with strong elastic bands. A
counter weight can be used to offset the unbalanced condition
with the heavy interface versus the light accelerometers.

Connect the tangential direction of the outer accelerometer
to CH1. Connect the radial direction of the outer accelerometer
to CH2. Connect the radial direction of the inner accelerometer
to CH3.

COMPUTER:

Launch Logger Pro. With a LabPro connected and the
accelerometers indicated above, a graph of the three
accelerations should be set up for you.

Set up data collection for 20 seconds at a rate of 20
samples per second.

Under Experiment, choose Remote then Setup. Follow
through until the LabPro is ready to collect data.

Disconnect the LabPro. When the right conditions are
arrived at, press the [START/STOP] button to
commence data collection.

Following data collection, re-connect the LabPro to the
computer and download the data.

CALCULATOR:

The calculator can be mounted on the LabPro with the
cradle.

Launch Datamate. The program should recognize the
accelerometers as you have them connected. If not, you will
have to go through Setup to get the program to recognize the
sensors.

Set up data collection for 20 seconds at 20 samples per
second (0.05 sec per sample).

The data will be available for examination and analysis
following the data run. It can be downloaded to a computer,
if desired, using a TI-Graph Link.

Start the wheel into motion. With practice, you will be
able to reach in and initiate data collection while it is
rotating. Keep the wheel moving with a constant angular speed
unless you wish to demonstrate the effect of speeding up or
slowing down where you get acceleration along the tangent.

Once the data collection is complete, stop the wheel and
either download or simply examine the data.

ANALYSIS

Plot the graphs as shown here to examine the data you have
collected

CH1 vs Time - shows the tangential acceleration (should
be approximately zero unless the wheel speeded up or slowed
down)

CH2 vs Time - shows the acceleration along the radius is
large. Should be able to determine the direction as being
inward.

CH2 and CH3 vs Time - shows the relationship between
radius and acceleration

EXTENSIONS

If one uses two accelerometers in a CBL case, mounted along
the length and width of the case, the procedure above can be
repeated with the experimenter holding the case at arm's length
and spinning. This doesn't yield the radial dependence of the
acceleration, but shows the tangential vs the radial very
clearly.

If the apparatus can be changed so the wheel moves
vertically without endangering the equipment, and if you can
drive it at a constant speed, the effects of going in a
vertical circle can be examined. This makes a good
approximation of the conditions in a common carnival or
amusement park ride. A counterweight is strongly
recommended.

TEACHER NOTES

We use the heavy wheel that we also use for gyroscope
demonstrations. A metal plate is mounted on a heavier piece of
particle board that has a hole conveniently located so we can
tighten up the nut used to secure the axle.

We have used two 1/4" plywood boards that we taped to the
spokes of a bicycle wheel. We have also mounted velcro pads on
one side to accept the velcro pads we place on the bottom of
the 3-axis accelerometers. This makes for convenient mounting,
and we use this technique throughout our labs.